It's got to be Smith. He's proven himself on all tracks in all countries. When his teammates were failing in England and Asia - swing and low spin - he was solid. He tends to fail when faced with extreme pace (SA and NZ), but because bowling standards are so low these days, he doesn't get exposed much. We need to see how he copes with Pakistan's new Test bowling unit.
Ketchim mentioned Amla; Amla is the best of the bunch in swinging conditions (he's probably the best test bat vs lateral movement since Dravid); he averages like 180+ vs Anderson and has never had a bad tour of England. Like Smith, he's also good in alien, subcon pitches (he was awful on his last tour to Asia, but that looked like burnout). His problem is that he tends to choke in big matches, and ICC tournaments, especially in ODIs (which his seemingly stella ODI record masks, as it masks most ODI openers). With ABDV gone, we might see Amla becoming more of a clutch player. This English tour will heavily determine Amla's reputation, I think.
Root hasn't proven himself outside of England yet. I think he will become England's greatest batsman, but he benefits from lots and lots of home games. He's done okay in India, NZ, SA and Aus, but mostly 40s-70s. Seems to be still finding his feet ouside of England. He's a home bully for the time being, which is normal for a youth.
Kane is the most underrated. Whenever he failed on a tour, on his second visit to that region he absolutely dominated. Good knocks in India is the only thing he's missing. I think he will retire with the most rounded record of the bunch. And while all these guys have big tons and double tons, Kane has them in the toughest conditions and vs strong attacks.
Cook is underrated too, and has the hardest task: opening often in England vs swinging new balls. He's also stellar on subcontinent pitches. Any average over 45 is great for a test opener. His batting is ugly and boring as hell though.
Kohli is the most overrated. Fails repeatedly vs good bowling or on tough tracks. Failed three times vs England, twice at home. Only piled on the runs in a bunch of flat track games vs Anderson and Rashid. Gets owned by Ali in India and Anderson in England. When the Aussies came to India specifically with lots of spinners, knowing India would have slow tracks which kill their pacers, he failed again. Tends to make runs on hard, bouncy, runs-truck pitches, but because those are found at the home's of great teams (SA and Australia), this makes him look like a beater of world class bowling. Of all the batsmen here, though, Kohli is the most serious and determined. So any weaknesses get quickly fixed and repaired and he crushes you the next time around.
Then there's ABDV, who recently quit test cricket. I don't think he will go down as a test great. He bailed on his team, hid down the order, and couldn't make runs in Australia anywhere other than Perth (fastest scoring ground in the country). Bad in Sri Lanka. Has only 1 good knock in India, 1 in England, none in New Zealand, and made all his away runs vs the weakest Pakistani and West Indies team ever. Still, one of the few South Africans not to choke in big ODIs.